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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Grant Proposal for the Continuation of the Voyager Interstellar Mission: LECP Investigation

This proposal documents the plans of the Low Energy Charged Particle (LECP) investigation team for participation in NASA's Voyager Interstellar Mission (VIM) as the Voyager 1 and 2 spacecraft explore the outer reaches of the heliosphere and search for the termination shock and the heliopause. The proposal covers the four year period from 1 January 1997 to 31 December 2000. The LECP instruments on Voyager 1 and 2 measure in situ intensities of charged particles with energies from about 30 keV to 100 MeV for ions, and about 20 keV to greater than 10 MeV for electrons. The instruments provide detailed spectral, angular, and compositional information about the particles. Composition is available for greater than 200 keV/nuc using multi-parameter measurements. Angular information is obtained by a mechanically scanned platform that rotates at various commanded rates. Measurements of low energy ion and electron intensities versus time and spatial location within the heliosphere contain an abundance of information regarding various transport and acceleration processes on both local (approx. 1 hr, approx. 0.01 AU) and global (approx. 11 yrs, approx. 100 AU) scales. The LECP instruments provide unique observations of such dynamical processes, and we anticipate that it will return critical information regarding the boundaries of the heliosphere. Several recent and exciting discoveries based on LECP measurements emphasize the important role that low energy charged particle distributions play in physical processes in the interplanetary medium. Yet, at the same time, these discoveries also underscore the fact that our understanding of processes in the outer heliosphere is, in most cases, incomplete, and in others, only rudimentary at best. Among the discoveries referred to above are the following: (1) Shocks: Examination of greater than 30 keV ion intensities have revealed: (a) a total absence of acceleration beyond only -100-200 keV at a strong transient shock in May 1991 at 35 AU, despite an enhanced level of seed particles; (b) a large transient shock in September 1991 of global scale, with intensities of shock-accelerated ions greater than or equal to 30 keV to approx. 30 MeV showing complex, highly energy-dependent spatial evolution, and small-scale (approx. few gyroradii), often anisotropic, micro-structures; (c) recurrent intensity increases in greater than or equal to 30 keV to -few MeV ions, with structures that, in some cases, show no correlation with the associated corotating shock. (2) Superthermal ion pressure: A global merged interaction region with a leading shock, downstream of which the superthermal ion (greater than or equal to 30 keV to approx. 4 MeV) pressure is comparable to that of the thermal plasma, and the total particle pressure yields a plasma beta of order unity. (3) Pickup ions: Measurements of the C/O ratio within transient structures at 35-45 AU showing the first clear evidence that transient shocks can pre-accelerate interstellar pickup ions from approx. 1 keV/nuc to at least 1 MeV/nuc. (4) Seed particles: Injection of ions for acceleration to high energies at the termination shock is unlikely to be a problem, since interplanetary transient and recurrent shocks are continually accelerating ions, of solar wind or interstellar origin, to highly superthermal energies. (5) Precursor electrons: Ambient solar electrons (greater than or equal to few tens of keV) that exist in the outer heliosphere ca form a broad precursor, several days wide, that is upstream of the termination shock and potentially observable a few months prior to the shock crossing. (6) Solar wind velocity at Voyager 1: We can use LECP ion data to obtain the solar wind velocity at Voyager 1, enabling us to provide critical measurement of the plasma flow as we approach and encounter the termination shock and other regions (necessary due to the partial failure of the Voyager 1 PLS experiment). The work of the LECP investigator team during the VIM will include: (1) Continuing operations with regard to the receipt, processing, verification, cataloging, display, and distribution of the data from the LECP instruments on Voyager 1 and 2, (2) Monitoring the health and performance of the LECP instruments, and evaluating and characterizing the response of the LECP instruments to various energetic particle and plasma environments, (3) Participating in, and supporting Voyager Project planning exercises and other coordinated activities relevant to exploration of the outer heliosphere, (4) Developing analysis techniques and operational procedures suitable for searching for and characterizing the boundaries and unique regions of the outher heliosphere, (5) Continuing the preparation of data sets appropriate for submission to the National Space Sciences Data Center (NSSDC) and, where appropriate, the Planetary Data System (PDS), (6) Maintaining direct Web access to online LECP data through the JHU/APL Voyager LECP home page, (7) Performing scientific evaluations of the Voyager 1 and 2 LECP data sets in conjunction with other data sets and other investigators, with particular focus on the outer regions of the heliosphere, and (8) Publishing the results of these evaluations in the scientific literature and presenting the results in scientific conferences.

Krimigis, Stamatios M.↗
NASA NTRS2002

Thermal Imaging of Convecting Opaque Fluids using Ultrasound

An ultrasound technique has been developed to non-intrusively image temperature fields in small-scale systems of opaque fluids undergoing convection. Fluids such as molten metals, semiconductors, and polymers are central to many industrial processes, and are often found in situations where natural convection occurs, or where thermal gradients are otherwise important. However, typical thermal and velocimetric diagnostic techniques rely upon transparency of the fluid and container, or require the addition of seed particles, or require mounting probes inside the fluid, all of which either fail altogether in opaque fluids, or necessitate significant invasion of the flow and/or modification of the walls of the container to allow access to the fluid. The idea behind our work is to use the temperature dependence of sound velocity, and the ease of propagation of ultrasound through fluids and solids, to probe the thermal fields of convecting opaque fluids non-intrusively and without the use of seed particles. The technique involves the timing of the return echoes from ultrasound pulses, a variation on an approach used previously in large-scale systems.

Xu, Hongzhou↗
NASA NTRS1984

Silicon production in an aerosol reactor

An aerosol reactor for the growth of large silicon particles by silane pyrolysis was shown to demonstrate the following properties: (1) generate seed particles by pyrolysis of a small amount of silane; (2) mix seed aerosol with primary silane flow, limiting number concentration such that the amount of silane is sufficient to grow the desired size of particles from the seed; and (3) react the silane at a rate which is controlled such that the seed particles scavenge the condensible vapors rapidly enough to inhibit further nucleation.

Wu, J. J.↗
NASA NTRS1987

Onset of runaway nucleation in aerosol reactors

The onset of homogeneous nucleation of new particles from the products of gas phase chemical reactions was explored using an aerosol reactor in which seed particles of silicon were grown by silane pyrolysis. The transition from seed growth by cluster deposition to catastrophic nucleation was extremely abrupt, with as little as a 17 percent change in the reactant concentration leading to an increase in the concentration of measurable particles of four orders of magnitude. From the structure of the particles grown near this transition, it is apparent that much of the growth occurs by the accumulation of clusters on the growing seed particles. The time scale for cluster diffusion indicates, however, that the clusters responsible for growth must be much smaller than the apparent fine structure of the product particles.

Wu, Jin Jwang↗
NASA NTRS2022

Advancing Solar Energetic Particle Forecasting

With growing interest from the aviation and satellite industries, and for NASA’s upcoming Artemis lunar missions, the need for improved scientific understanding and accurate forecasting of solar energetic particle events has never been stronger. In this paper we discuss the observational, validation and model transition support required to achieve these goals. Well-calibrated, high-quality energetic electron, proton, and ion measurements are essential. Expansions to the fields of view offered by current X-ray, extreme ultraviolet and coronagraph instruments, to obtain increased coverage of the solar corona and heliosphere, from vantage points off the Sun-Earth line, are desired for model input. New observations of suprathermal particles are needed to characterize seed particle distributions and low latency space-based observations of solar radio emissions are also desired. Together, this observational suite should offer high cadence, low latency, reliable and accurate space weather data streams. Consistent, extensive and quantitative model validation is required to assess scientific advancements and pave the way for models transitioning to real-time forecast operations. Model performance and skill should be compared to observations and to current operational forecasting baselines. Finally, resources are required to support the significant effort of transitioning mature models into forecast operations.

solar energetic particles↗
NASA NTRS1987

First-order Fermi acceleration in the two-stream limit

A study of the first-order Fermi mechanism for accelerating cosmic-rays at relativistic and nonrelativistic shocks is carried out by using the two-stream approximation. Exact steady-state analytic solutions illustrating the shock acceleration process in the test-particle limit in which monoenergetic (relativistic) seed particles enter the shock through an upstream free-escape boundary are obtained. The momentum spectrum of the shock accelerated particles consists of a series of Dirac delta distributions corresponding to particles that have undergone an integral number of acceleration cycles. Since particles in the model have a finite fixed escape probability from the shock and the particle momenta p are equally spaced in log p, the envelope of the delta functions series is a power law in momentum. The solutions are used to discuss time-dependent aspects of the shock acceleration process in terms of the finite cycle time, escape probability, and momentum change per cycle that can be deduced from the steady-state model. The length-scale over which the accelerated particles extend upstream of the shock is shown to depend upon the particle energy, with the higher energy particles extending further upstream. This effect is shown to be intimately related to the kinematic threshold requirement that the particle speed exceed the fluid speed in order for particles to swim upstream of the shock and participate in the shock acceleration process.

Bogdan, T. J.↗
NASA NTRS2002

Measurements of Turbulence Attenuation by a Dilute Dispersion of Solid Particles in Homogeneous Isotropic Turbulence

This research addresses turbulent gas flows laden with fine solid particles at sufficiently large mass loading that strong two-way coupling occurs. By two-way coupling we mean that the particle motion is governed largely by the flow, while the particles affect the gas-phase mean flow and the turbulence properties. Our main interest is in understanding how the particles affect the turbulence. Computational techniques have been developed which can accurately predict flows carrying particles that are much smaller than the smallest scales of turbulence. Also, advanced computational techniques and burgeoning computer resources make it feasible to fully resolve very large particles moving through turbulent flows. However, flows with particle diameters of the same order as the Kolmogorov scale of the turbulence are notoriously difficult to predict. Some simple flows show strong turbulence attenuation with reductions in the turbulent kinetic energy by up to a factor of five. On the other hand, some seemingly similar flows show almost no modification. No model has been proposed that allows prediction of when the strong attenuation will occur. Unfortunately, many technological and natural two-phase flows fall into this regime, so there is a strong need for new physical understanding and modeling capability. Our objective is to study the simplest possible turbulent particle-laden flow, namely homogeneous, isotropic turbulence with a uniform dispersion of monodisperse particles. We chose such a simple flow for two reasons. First, the simplicity allows us to probe the interaction in more detail and offers analytical simplicity in interpreting the results. Secondly, this flow can be addressed by numerical simulation, and many research groups are already working on calculating the flow. Our detailed data can help guide some of these efforts. By using microgravity, we can further simplify the flow to the case of no mean velocity for either the turbulence or the particles. In fact the addition of gravity as a variable parameter may help us to better understand the physics of turbulence attenuation. The experiments are conducted in a turbulence chamber capable of producing stationary or decaying isotropic turbulence with nearly zero mean flow and Taylor microscale Reynolds numbers up to nearly 500. The chamber is a 410 mm cubic box with the corners cut off to make it approximately spherical. Synthetic jet turbulence generators are mounted in each of the eight corners of the box. Each generator consists of a loudspeaker forcing a plenum and producing a pulsed jet through a 20 mm diameter orifice. These synthetic jets are directed into ejector tubes pointing towards the chamber center. The ejector tubes increase the jet mass flow and decrease the velocity. The jets then pass through a turbulence grid. Each of the eight loudspeakers is forced with a random phase and frequency. The resulting turbulence is highly Isotropic and matches typical behavior of grid turbulence. Measurements of both phases are acquired using particle image velocimetry (PIV). The gas is seeded with approximately 1 micron diameter seeding particles while the solid phase is typically 150 micron diameter spherical glass particles. A double-pulsed YAG laser and a Kodak ES-1.0 10-bit PIV camera provide the PIV images. Custom software is used to separate the images into individual images containing either gas-phase tracers or large particles. Modern high-resolution PIV algorithms are then used to calculate the velocity field. A large set of image pairs are acquired for each case, then the results are averaged both spatially and over the ensemble of acquired images. The entire apparatus is mounted in two racks which are carried aboard NASA's KC-135 Flying Microgravity Laboratory. The rack containing the turbulence chamber, the laser head, and the camera floats freely in the airplane cabin (constrained by competent NASA personnel) to minimize g-jitter.

Eaton, John↗
NASA NTRS2008

Virtual Energetic Particle Observatory (VEPO)

The Virtual Energetic Particle Observatory (VEPO) focuses on improved discovery, access, and usability of heliospheric energetic particle and ancillary data products from selected spacecraft and sub-orbital instruments of the heliophysics data environment. The energy range of interest extends over the full range of particle acceleration from keV energies of suprathermal seed particles to GeV energies of galactic cosmic ray particles. Present spatial coverage is for operational and legacy spacecraft operating from the inner to the outer heliosphere, e.g. from measurements by the two Helios spacecraft to 0.3 AU to the inner heliosheath region now being traversed by the two Voyager spacecraft. This coverage will eventually be extended inward to ten solar radii by the planned NASA solar probe mission and at the same time beyond the heliopause into the outer heliosheath by continued Voyager operations. The geospace fleet of spacecraft providing near-Earth interplanetary measurements, selected magnetospheric spacecraft providing direct measurements of penetrating interplanetary energetic particles, and interplanetary cruise measurements from planetary spacecraft missions further extend VEPO resources to the domain of geospace and planetary interactions. Ground-based (e.g., neutron monitor) and high-altitude suborbital measurements can expand coverage to the highest energies of galactic cosmic rays affected by heliospheric interaction and of solar energetic particles. Science applications include investigation of solar flare and coronal mass ejection events. acceleration and transport of interplanetary particles within the inner heliosphere, cosmic ray interactions with planetary surfaces and atmospheres, sources of suprathermal and anomalous cosmic ray ions in the outer heliosphere, and solar cycle modulation of galactic cosmic rays. Robotic and human exploration, and eventual habitation, of planetary and space environments beyond the Earth require knowledge of radiation hazards informed by VEPO data resources. The VEPO project has completed the first year of work to define science requirements, to document and register selected data products in SPASE format while evolving SPASE for increased applicability to VEPO data, and to support enhanced discovery and access for these products through the evolving data query and middleware system of the Virtual Heliospheric Observatory (VHO). The VEPO team operates as a heliophysics focus group for energetic particle data resources in partnership with VHO and also leverages existing data services of NASA's Space Physics Data Facility. We invite comments from the U.S. and international data provider and user communities on review of the current VEPO/VHO user interface, on directions for future evolution of VEPO and supporting data systems including VHO and SPDF, and on relations to other elements of the heliophysics virtual observatory environment.

Cooper, John F.↗
NASA NTRS2016

Particle Streak Velocimetry of Supersonic Nozzle Flows

A novel velocimetry technique to probe the exhaust flow of a laboratory scale combustor is being developed. The technique combines the advantages of standard particle velocimetry techniques and the ultra-fast imaging capabilities of a streak camera to probe high speed flows near continuously with improved spatial and velocity resolution. This "Particle Streak Velocimetry" technique tracks laser illuminated seed particles at up to 236 picosecond temporal resolution allowing time-resolved measurement of one-dimensional flows exceeding 2000 m/s as are found in rocket nozzles and many other applications. Developmental tests with cold nitrogen have been performed to validate and troubleshoot the technique with supersonic flows of much lower velocity and without background noise due to combusting flow. Flow velocities on the order of 500 m/s have been probed with titanium dioxide particles and a continuous-wave laser diode. Single frame images containing multiple streaks are analyzed to find the average slope of all incident particles corresponding to the centerline axial flow velocity. Long term objectives for these tests are correlation of specific impulse to theoretical combustion predictions and direct comparisons between candidate green fuels and the industry standard, monomethylhydrazine, each tested under identical conditions.

Willits, J. D.↗
NASA NTRS1992

Removing Undesired Fine Powder From Silicon Reactor

Fluidized-bed reactor produces highly pure polycrystalline silicon particles with diameters approximately greater than 400 micrometers. Operates by pyrolysis of silane in reaction zone, which is bed of silicon seed particles fluidized by flow of silane and carrier gas. Above reaction zone, gas mixture flows rapidly enough to entrain silicon powders, but not larger seed and product particles. Entrained particles swept out of reactor. Applicable to other processes such as production of fine metal and ceramic powders where control of sizes of product needed.

Flagella, Robert N.↗
NASA NTRS1981

Development of processes for the production of solar grade silicon from halides and alkali metals, phase 1 and phase 2

High temperature reactions of silicon halides with alkali metals for the production of solar grade silicon are described. Product separation and collection processes were evaluated, measure heat release parameters for scaling purposes and effects of reactants and/or products on materials of reactor construction were determined, and preliminary engineering and economic analysis of a scaled up process were made. The feasibility of the basic process to make and collect silicon was demonstrated. The jet impaction/separation process was demonstrated to be a purification process. The rate at which gas phase species from silicon particle precursors, the time required for silane decomposition to produce particles, and the competing rate of growth of silicon seed particles injected into a decomposing silane environment were determined. The extent of silane decomposition as a function of residence time, temperature, and pressure was measured by infrared absorption spectroscopy. A simplistic model is presented to explain the growth of silicon in a decomposing silane enviroment.

Dickson, C. R.↗
NASA NTRS1986

Fluidized-bed reactor modeling for production of silicon by silane pyrolysis

An ideal backmixed reactor model (CSTR) and a fluidized bed bubbling reactor model (FBBR) were developed for silane pyrolysis. Silane decomposition is assumed to occur via two pathways: homogeneous decomposition and heterogeneous chemical vapor deposition (CVD). Both models account for homogeneous and heterogeneous silane decomposition, homogeneous nucleation, coagulation and growth by diffusion of fines, scavenging of fines by large particles, elutriation of fines and CVD growth of large seed particles. At present the models do not account for attrition. The preliminary comparison of the model predictions with experimental results shows reasonable agreement. The CSTR model with no adjustable parameter yields a lower bound on fines formed and upper estimate on production rates. The FBBR model overpredicts the formation of fines but could be matched to experimental data by adjusting the unkown jet emulsion exchange efficients. The models clearly indicate that in order to suppress the formation of fines (smoke) good gas-solid contacting in the grid region must be achieved and the formation of the bubbles suppressed.

Dudukovic, M. P.↗
NASA NTRS2013

In Situ Solid Particle Generator

Particle seeding is a key diagnostic component of filter testing and flow imaging techniques. Typical particle generators rely on pressurized air or gas sources to propel the particles into the flow field. Other techniques involve liquid droplet atomizers. These conventional techniques have drawbacks that include challenging access to the flow field, flow and pressure disturbances to the investigated flow, and they are prohibitive in high-temperature, non-standard, extreme, and closed-system flow conditions and environments. In this concept, the particles are supplied directly within a flow environment. A particle sample cartridge containing the particles is positioned somewhere inside the flow field. The particles are ejected into the flow by mechanical brush/wiper feeding and sieving that takes place within the cartridge chamber. Some aspects of this concept are based on established material handling techniques, but they have not been used previously in the current configuration, in combination with flow seeding concepts, and in the current operational mode. Unlike other particle generation methods, this concept has control over the particle size range ejected, breaks up agglomerates, and is gravity-independent. This makes this device useful for testing in microgravity environments.

Agui, Juan H.↗
NASA NTRS1980

Stratospheric aerosol modification by supersonic transport and space shuttle operations - Climate implications

The potential effects on stratospheric aerosols of supersonic transport emissions of sulfur dioxide gas and submicron soot granules, and space shuttle rocket emissions of aluminum oxide particulates are estimated. An interactive particle-gas model of the stratospheric aerosol layer is used to calculate changes due to exhaust emissions, and an accurate radiation transport model is employed to compute the effect of aerosol changes on the earth's average surface temperature. It is concluded that the release of large numbers of small particles (soot or aluminum oxide) into the stratosphere should not lead to a corresponding significant increase in the concentration of large, optically active aerosols, but that the increase in large particles is severely limited by the total mass of sulfate available to make large particles in situ, and by the rapid loss of small seed particles via coagulation. We find that a fleet of several hundred advanced supersonic aircraft operating daily at 20 km, or the launch of one space shuttle rocket per week, could produce roughly a 20% increase in the large-particle concentration of the stratosphere. We find, in addition, that aerosol increases of this magnitude would reduce the global surface temperature by less than 0.01 K.

Turco, R. P.↗
NASA NTRS1991

Particle displacement tracking applied to air flows

Electronic Particle Image Velocimeter (PIV) techniques offer many advantages over conventional photographic PIV methods such as fast turn around times and simplified data reduction. A new all electronic PIV technique was developed which can measure high speed gas velocities. The Particle Displacement Tracking (PDT) technique employs a single cw laser, small seed particles (1 micron), and a single intensified, gated CCD array frame camera to provide a simple and fast method of obtaining two-dimensional velocity vector maps with unambiguous direction determination. Use of a single CCD camera eliminates registration difficulties encountered when multiple cameras are used to obtain velocity magnitude and direction information. An 80386 PC equipped with a large memory buffer frame-grabber board provides all of the data acquisition and data reduction operations. No array processors of other numerical processing hardware are required. Full video resolution (640x480 pixel) is maintained in the acquired images, providing high resolution video frames of the recorded particle images. The time between data acquisition to display of the velocity vector map is less than 40 sec. The new electronic PDT technique is demonstrated on an air nozzle flow with velocities less than 150 m/s.

Wernet, Mark P.↗
NASA NTRS1991

Particle displacement tracking applied to air flows

Electronic Particle Image Velocimetric (PIV) techniques offer many advantages over conventional photographic PIV methods such as fast turn around times and simplified data reduction. A new all electronic PIV technique was developed which can measure high speed gas velocities. The Particle Displacement Tracking (PDT) technique employs a single CW laser, small seed particles (1 micron), and a single intensified, gated CCD array frame camera to provide a simple and fast method of obtaining two-dimensional velocity vector maps with unambiguous direction determination. Use of a single CCD camera eliminates registration difficulties encountered when multiple cameras are used to obtain velocity magnitude and direction information. An 80386 PC equipped with a large memory buffer frame-grabber board provides all of the data acquisition and data reduction operations. No array processors of other numerical processing hardware are required. Full video resolution (640 x 480 pixel) is maintained in the acquired images, providing high resolution video frames of the recorded particle images. The time between data acquisition to display of the velocity vector map is less than 40 sec. The new electronic PDT technique is demonstrated on an air nozzle flow with velocities less than 150 m/s.

Wernet, Mark P.↗
NASA NTRS2005

Fuzzy Logic Particle Tracking

A new all-electronic Particle Image Velocimetry technique that can efficiently map high speed gas flows has been developed in-house at the NASA Lewis Research Center. Particle Image Velocimetry is an optical technique for measuring the instantaneous two component velocity field across a planar region of a seeded flow field. A pulsed laser light sheet is used to illuminate the seed particles entrained in the flow field at two instances in time. One or more charged coupled device (CCD) cameras can be used to record the instantaneous positions of particles. Using the time between light sheet pulses and determining either the individual particle displacements or the average displacement of particles over a small subregion of the recorded image enables the calculation of the fluid velocity. Fuzzy logic minimizes the required operator intervention in identifying particles and computing velocity. Using two cameras that have the same view of the illumination plane yields two single exposure image frames. Two competing techniques that yield unambiguous velocity vector direction information have been widely used for reducing the single-exposure, multiple image frame data: (1) cross-correlation and (2) particle tracking. Correlation techniques yield averaged velocity estimates over subregions of the flow, whereas particle tracking techniques give individual particle velocity estimates. For the correlation technique, the correlation peak corresponding to the average displacement of particles across the subregion must be identified. Noise on the images and particle dropout result in misidentification of the true correlation peak. The subsequent velocity vector maps contain spurious vectors where the displacement peaks have been improperly identified. Typically these spurious vectors are replaced by a weighted average of the neighboring vectors, thereby decreasing the independence of the measurements. In this work, fuzzy logic techniques are used to determine the true correlation displacement peak even when it is not the maximum peak, hence maximizing the information recovery from the correlation operation, maintaining the number of independent measurements, and minimizing the number of spurious velocity vectors. Correlation peaks are correctly identified in both high and low seed density cases. The correlation velocity vector map can then be used as a guide for the particle-tracking operation. Again fuzzy logic techniques are used, this time to identify the correct particle image pairings between exposures to determine particle displacements, and thus the velocity. Combining these two techniques makes use of the higher spatial resolution available from the particle tracking. Particle tracking alone may not be possible in the high seed density images typically required for achieving good results from the correlation technique. This two-staged velocimetric technique can measure particle velocities with high spatial resolution over a broad range of seeding densities.

Source record↗
NASA NTRS1976

Influence of particle drag coefficient on particle motion in high-speed flow with typical laser velocimeter applications

The effect of using different particle drag coefficient C sub D equations for computing the velocity of seeded particles in high-speed gas flows was investigated. The C sub D equations investigated included the Stokes equation, a second incompressible equation valid for higher relative Reynolds numbers, and six equations that account for the effects of compressibility together with the effects of relative Reynolds numbers greater than one. The flows investigated were center-line nozzle flows, normal shocks, and oblique shocks for free-stream Mach numbers of 1.6 to 6 and stagnation pressures of 1 and 3.4 atmospheres. The net result was empirical C sub D equation based on the latest sphere C sub D data for the low relative Mach number and Reynolds number conditions that are encountered in supersonic flows.

Walsh, M. J.↗